Steady-state optimizing control

Latour, P., Use of steady-state optimization for computer control in the process industries. In On-line Optimization Techniques in Industrial Control (Kompass, E. J. and Williams, T. J., eds.). Technical Publishing Company, 1979. 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

Bahri, P Bandoni, A., and Romagnoli, J. A. (1996). Effect of disturbances in optimizing control Steady-state open-loop backoff problem. AIChE J. 42,983-995. 

Process design modifications usually have a bigger impact on operability (dynamic resilience). Dynamic resilience depends on controller structure, choice of measurements, and manipulated variables. Multivariable frequency-response techniques have been used to determine resilience properties. A primary result is that closed-loop control quality is limited by system invertability (nonmin-imum phase elements). Additionally, it has been shown that steady-state optimal designs are not necessarily optimal in dynamic operation. 

This problem is obviously a large one in that it includes all the problems of optimal control with uncertain parameters as well as embedding in synthesis. Two example problems are given, with one illustrating that the minimax structure may well be different from the steady-state optimal structure. 

Arkun, Y., Stephanopoulos, G. and Morari, M., "Design of Steady-State Optimizing Control Structures for Chemical Processes," AlChE 71st Annual Meeting, Miami Beach, FL., November 12-lb, 1978. 

Since the plant is decomposed to its subsystems, the steady-state optimization problem is characterized by a multiechelon structure where the subsystem optimizing controllers communicate with a coordinator. For further details the reader is referred to the work by Arkun (20). 

Steady State Optimizing Control of a Fluid Catalytic Cracker. The process model used in this example can be found in (21) while the design parameters are given in (20). The important constraints are T e reactor temperature 930°F, T = regenerator... 

By calculating TACs for a range of values of Vr and Nj, the minimum steady-state optimal plant turns out to have a reactor holdup of 3000 Ib-mol and a stripper with 19 trays. With no consideration of dynamic controllability, this is the best plant. 

Use the remaining control valves for either steady-state optimization (minimize energy, maximize yield, etc.) or to improve dynamic controllability. A common example is controlling purities of recycle streams. Even though these streams... 

Chapter 2 treats the topic of steady-state optimization. Necessary conditions for extrema of functions are derived using variational principles. These steady-state optimization techniques are used for the determination of optimal setpoints for regulators used in supervisory computer control. 

Skogestad, S. (2000 ), Self-optimizing control the missing link between steady-state optimization and control . Comp. Chem. Engng. 24,569-575. 

It should be observed that as in the case of linear back-off synthesis, a steady state optimization problem is solved to determine the topology of the process and the controller. A dynamic optimization problem is then solved to determine the optimal value of the continuous optimization variables. The algorithm iterates between the steady state mixed integer... 

A steady-state optimization is then performed on the modules to identify any active constraints present in the module [46], The optimization is carried out over the expected range of disturbances subject to satisfying any process and operational constraints. All identified active control constraints are considered to be variables, whieh during the development of the control structure should be controlled in order to achieve reasonable performance. 

Based on the steady-state optimization for each module, only one active control constraint is identified for the HDA process - the reactor inlet temperature. The nine-step procedure to generate a plantwide control structure developed by Luyben et al.[7] is now applied to each module. These steps are (i) establish the control objectives, (ii) determine the control degrees of freedom, (iii) establish energy management, (iv) set the production rate, (v) control the product quality, (vi) fix a flow in every recycle loop and control inventories, (vii) check component balances and (viii) control individual imit operations, and (ix) optimize the economics or improve the dynamic controllability. The number of control degrees of freedom identified for each module (referred to by their respective dominant unit operation) are as follows reactor 10, product column 10, and recycle column 5. 

Skogestad, S., Self-optimizing Control The Missing Link Between Steady-State Optimization and Control. Compute Chem. Eng., 24, 569 (2000). 

As indicated in Section 20.1 and Fig. 20.9, the MFC calculations at each control execution time are typically performed in two steps. First, the optimum set points (or targets) for the control calculations are determined. Then, a set of M control moves are generated by the control calculations, and the first move is implemented. In practical applications, significant economic benefits result from both types of calculations, but the steady-state optimization is usually more important. In this section, the set-point calculations are described in more detail. 

The MFC set points are calculated so that they maximize or minimize an economic objective function. The calculations are usually based on linear steady-state models and a simple objective function, typically a linear or quadratic function of the MVs and CVs. The linear model can be a linearized version of a complex nonlinear model or the steady-state version of the dynamic model that is used in the control calculations. Linear inequality constraints for the MVs and CVs are also included in the steady-state optimization. The set-point calculations are repeated at each sampling instant because the active constraints can change frequently due to disturbances, instrumentation, equipment availability, or varying process conditions. 

We have emphasized that the goal of this steady-state optimization is to determine ysp and Usp, the set points for the control calculations in Step 6 of Fig. 20.9. But why not use yref and iiref for this purpose The reason is that yref and iiref are ideal values that may not be attainable for the current plant conditions and constraints, which could have changed since yref and iiref were calculated. Thus, steady-state optimization (Step 5) is necessary to calculate ysp and Usp, target values that more accurately reflect current conditions. In Eq. 20-68, ysp and Usp are shown as the independent values for the optimization. However, ysp can be eliminated by substituting the steady-state model, ysp = Kusp. 

Model predictive control is an important model-based control strategy devised for large multiple-input, multiple-output control problems with inequality constraints on the inputs and/or outputs. This chapter has considered both the theoretical and practical aspects of MFC. Applications typically involve two types of calculations (1) a steady-state optimization to determine the optimum set points for the control calculations, and (2) control calculations to determine the MV changes that will drive the process to the set points. The success of model-based control strategies such as MFC depends strongly on the availability of a reasonably accurate process model. Consequently, model development is the most critical step in applying MFC. As Rawlings (2000) has noted, feedback can overcome some effects... 

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